One way is to either put a 100% wet delay on an aux channel and a send to it on the vocal track, then manually automate the send level as required. Another is to automate the delay wet/dry mix. Time consuming but using automation envelopes like this often gives more controllable results than the sidechain and compressor method.
"Automatic" ducking using a sidechained compressor works like this-
Create an aux track with a 100 wet delay on it and a side-chainable compressor (which will do the ducking) after the delay.
Set up a send on the vocal track that feeds the compressor sidechain and another that feeds the delay's aux channel.
The send to the aux channel will be used to set how much of the vocal track gets processed by the delay, just like usual. So switch off the compressor and set the track-> channel send and the delay plugin to give the amount of delay you want.
Now switch the compressor on. Set the side-chain send on the vocal track so the vocals are triggering the compressor. Then lower the compressor threshold and increase its ratio until you get the effect you want.
You'll probably find it takes quite a bit of adjusting the send(s), delay and compressor settings, including threshold and release, to get things sounding the way you want.
Or invest in a delay that has an adjustable ducking function. BozDigital's delay has one that's quite adjustable.
Personally I use the delay+compressor method when monitoring tracking, but afterwards either remove the compressor and create envelopes to control the delay, or if the compressor method is pretty much right already automate the compressor as required for fine control.
There are other ways to get a ducking delay or reverb, but those are probably the simplest.